Fully merge two objects?
Delete the edges between both objects;
Click one of the vertices of one of the ends of the objects that you want to connect, and use Shift+s → Cursor to selected, so we can use the 3D cursor's location to move the other object to the exact position of its counterpart.
Since for me the 3D cursor snapped to one of the wrong vertices, I quickly separated the object using p, then g and z to grab it along its Z-axis, and it snapped right in place.
Select both objects, use Ctrl+j to join.
Remove the faces that are currently between the vertices you want to get rid of.
Select the vertices surrounding the deleted faces, and navigate to Mesh → Clean Up → Merge by distance, and tweak the value to delete the 14 double vertices (by turning it all the way down).
Now select the vertices that are left, click Del, and select the Edge Loops option.

Both models are now joined and clean:

(Note: I rotated the model so it fits this page better in most cases.)